Free-convection flow through an annular porous medium

This study addresses the Brinkman-extended Darcy model (Brinkman flow) of a laminar free-convective flow in an annular porous region. Closed form expressions for Velocity field, Temperature field, Skin-friction and Mass flow rate are given, under a thermal boundary condition of mixed kind at the outer surface of the inner cylinder while the inner surface of the outer cylinder is isothermal. The governing independent parameters are identified to be Darcy number (Da) and ratio of outer to inner radii (R). It is hoped that the study of such flows gives limiting conditions for developing flows and provides an analytical check on numerical solutions for more complex problems dealing with non-Darcian free-convection flow in an annular region.